This invention relates to an electronic musical instrument adapted to generate anharmonic overtones.
The tone of a natural musical instrument generally contains overtone components which are not in a true harmonic relationship with respect to the fundamental wave component and such overtone components characterize the tone. An electronic musical instrument designed to generate such anharmonic overtones is disclosed in the specification of the U.S. Pat. No. 3,888,153. However, the invention disclosed herein has the following limitation in the anharmonic overtone of the tone generated. The Fourier component amplitude F.sup.(n) of the musical tone is calculated according to the following equation: EQU F.sup.(n) = Cn sin .pi./W (nqR + .upsilon. Jq) . . . (1)
where n represents the order of the Fourier component, that is n = 1, 2 . . . w, Cn the amplitude coefficient of the Fourier component, q time element which increases 1, 2, 3 . . . at a predetermined time interval, R a value proportional to the fundamental frequency of the musical tone .upsilon. a value corresponding to the order of the Fourier component and being expressed by .upsilon. = n - 1, and J a constant thus the amount [nqR] corresponding to the phases of the respective Fourier components having accurate harmonic relationship and the amount [.upsilon.jq] representing phase deviations for the respective Fourier components to realize resultant frequency deviations of the harmonics from the true harmonic relationship. Thus, anharmonic overtones are obtained by adding the deviation component [.upsilon.jq] to the true harmonic components. However, in this method, the element that determines the frequency deviation is only the constant J and a relationship between frequency deviations of respective overtone components is always so that it is impossible to independently determine the amount of the frequency deviation of the respective overtones. In other words, as shown in Table 1, the fundamental wave has no deviation, the second harmonic has a deviation of Jq, and the amount of frequency deviation increases with the order of the harmonics.
Table I ______________________________________ order of overtones amount of frequency n deviation .nu.Jq ______________________________________ 1 (1 - 1) Jq = 0 2 Jq 3 2Jq 4 3Jq . . . . n (n - 1) Jq ______________________________________
In other words, overtones of the higher orders always have larger frequency deviations than the overtones of the lower orders. Accordingly, with the method described above, the relationship in the anharmonic property between respective overtones (partials) is always constant so that there is limitation in the musical tone (anharmonic overtone) that can be produced.